Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as “frailty variation”. Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being crucial to protect vulnerable individuals from severe outcomes as the virus becomes endemic

Scheduling with Sequencing Flexibility *

This study examines the effects of sequencing flexibility on the performance of rules used to schedule operations in manufacturing systems. The findings show that taking advantage of even low levels of sequencing flexibility in the set of operations required to do a job results in substantial improvement in the performance of scheduling rules with respect to mean flowtime. Differences in the mean flowtime measure for various rules also diminish significantly with increasing sequencing flexibility. Performance improvements additionally result for such due-date related performance measures as mean tardiness and the proportion of jobs tardy. At high levels of sequencing flexibility, some nonparametric scheduling rules outperform the shortest processing time rule in terms of the mean flowtime criterion. Rules based on job due dates also outperform rules based on operation milestones in terms of tardiness related criteria at high levels of sequencing flexibility. The implications of these findings for the design of manufacturing systems and product design are noted.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73893/1/j.1540-5915.1993.tb00477.x.pd

Throughput analysis in an automated material handling system

Throughput analysis in an automated material handling system, such as an Automated Storage and Retrieval System(AS/RS), may be a complex problem. In the past, several approaches have been used for such an analysis. This paperpresents a combinatorial ap proach to evaluating the throughput performance of a mini-load system, with simulation as the primary method of investigation.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.Comment: v4: Minor changes made following helpful comments by the referee

Perfect Hash Families: The Generalization to Higher Indices

Perfect hash families are often represented as combinatorial arrays encoding partitions of kitems into v classes, so that every t or fewer of the items are completely separated by at least a specified number of chosen partitions. This specified number is the index of the hash family. The case when each t-set must be separated at least once has been extensively researched; they arise in diverse applications, both directly and as fundamental ingredients in a column replacement strategy for a variety of combinatorial arrays. In this paper, construction techniques and algorithmic methods for constructing perfect hash families are surveyed, in order to explore extensions to the situation when each t-set must be separated by more than one partition.https://digitalcommons.usmalibrary.org/books/1029/thumbnail.jp

A History of Discrete Event Simulation Programming Languages

The history of simulation programming languages is organized as a progression in periods of similar developments. The five periods, spanning 1955-1986, are labeled: The Period of Search (1955-1960); The Advent (1961-1965); The Formative Period (1966-1970); The Expansional Period (1971-1978); and The Period of Consolidation and Regeneration (1979-1986). The focus is on recognizing the people and places that have made important contributions in addition to the nature of the contribution. A balance between comprehensive and in-depth treatment has been reached by providing more detailed description of those languages which have or have had major use. Over 30 languages are mentioned, and numerous variations are described in the major contributors. A concluding summary notes the concepts and techniques either originating with simulation programming languages or given significant visibility by them